Please help please make sure you have a clear hand writing.

Make sure you read all the questions carefully and answer all the questions.

1.) The derivative rule for a polynomial term y = f(x) = Cxⁿ+ Kx⁰ = Cxⁿ + K is

dy/dx = f '(x) = Cnx^n-1+ 0

Therefore, if we know the derivative, we can reconstruct the function only to an unknown constant K. That means that f'(x) implies f(x) + K, where K is any constant. When K is unknown, then we have a "family" of solutions instead of a single solution.

Let f '(x) = x + 2

a.) What is f(x) ? (be sure to include the + K term).

b.) Write the equations for 3 members of the solution family. Use 3 different values of K.)

c.) Plot these 3 members of the family of solutions for f(x).

d.) Determine K for the family member that goes through the point (0,2).

e.) In terms of the general transformation equation

(y - k) = A f[B(x-h)]

how are the different family members related to each other?

Choose one from the following 4 answers.

1.) By a horizontal shift

2.) By a vertical shift

3.) By an expansion along the y axis

4.) By a compression along the x axis

8.) Given the graph in the following figure. Fill in the table for the values of the slope f'(x) and the curvature/concavity f''(x).

(-1, 5) 5 4 3 2 1 (0, 1) -2 -1 0 2 -1- -2- -3 (1, -3)